question_answer

The system shown is in equilibrium. All the strings and pulleys are massless. Instantaneous acceleration of A, B and C when string above B is cut are, respectively,

 

A) \[0,\,2g,\,2g\]  

B) \[0,\,2g,\,g\]              

C) \[0,2g,0\]               

D) \[g,g,2g\]

Correct Answer: A

Solution :

  [a] Spring force in spring 2 before cutting \[=2mg\] Spring force in spring 1 before cutting \[=mg\] Just after cutting, the spring forces do not change. For A:   \[{{k}_{2}}x-2mg=2m{{a}_{A}}\Rightarrow {{a}_{A}}=0\] For B:  \[{{k}_{2}}x+2mg=4mg=2m{{a}_{B}}\Rightarrow {{a}_{B}}=2g\] For C: \[{{k}_{1}}x+mg=2mg=mac\Rightarrow ac=2g\]